Bicycle Frame Geometry I - Tube Lengths

Use the geometry generator applet below to help you with the exercises on this page.

As you will see later in the module, the bicycle frame geometry significantly affects how the frame members are loaded. This applet allows you to redesign the shape of the bicycle by dragging on the joints. As you do so the x and y coordinates of the joints (shown) will be updated. In doing so, you will also be affecting the length of the tube members.

Drag the joints so that the top tube (between the seat and the handlebars) is horizontal (any length is OK). What is similar between the coordinates of the two joints? Suppose you were constructing a bike based on your design, what length of steel would you need for the top tube?

Now move the joint nearest the handlebars upwards a bit so that the top tube is no longer vertical. Now what is the length of the top tube? It is not as easy to determine, perhaps, as it was when the tube was horizontal. Use the concept of position vectors to help you determine it.

In addition find the current lengths of the other tube members. Once again, check your answers with the applet.

Once you have verified the tube member lengths for the current frame shape, continue dragging the joints on the frame and see if you can understand how changing the joint coordinates changes the tube lengths.


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